Advertisements
Advertisements
प्रश्न
Find the general solution of the following equation:
Advertisements
उत्तर
Given,
sin 3x + cos 2x = 0
We know that: sin θ = cos `(π/2 - theta)`
∴ cos 2x = −sin 3x
⇒ cos 2x = −cos`(pi/2- 3x)`
We know that: −cos θ = cos (π – θ)
∴ cos 2x = cos`(pi - (pi/2 - 3x))`
⇒ cos 2x cos `(pi/2 + 3x)`
If cos x = cos y, implies x = 2nπ ± y, where n ∈ Z.
From above expression and on comparison with standard equation we have:
`y = (pi/2 + 3x)`
∴ 2x = 2nπ ± `(pi/2 + 3x)`
Hence,
`2x = 2npi + pi/2 + 3x or 2x = 2npi - pi/2 - 3x`
∴ `x = -pi/2 - 2npi or 5x = 2npi - pi/2`
⇒ `x = -pi/2 (1 + 4n) or x = pi/10 (4n - 1)`
∴ `x = -pi/2 (4n + 1) or pi/10 (4n - 1)`, where n ∈ Z
APPEARS IN
संबंधित प्रश्न
If \[\sin x = \frac{a^2 - b^2}{a^2 + b^2}\], then the values of tan x, sec x and cosec x
If \[\tan x = \frac{b}{a}\] , then find the values of \[\sqrt{\frac{a + b}{a - b}} + \sqrt{\frac{a - b}{a + b}}\].
If \[a = \sec x - \tan x \text{ and }b = cosec x + \cot x\], then shown that \[ab + a - b + 1 = 0\]
If \[T_n = \sin^n x + \cos^n x\], prove that \[2 T_6 - 3 T_4 + 1 = 0\]
Prove that:
In a ∆ABC, prove that:
In a ∆A, B, C, D be the angles of a cyclic quadrilateral, taken in order, prove that cos(180° − A) + cos (180° + B) + cos (180° + C) − sin (90° + D) = 0
Prove that:
If \[\frac{\pi}{2} < x < \pi, \text{ then }\sqrt{\frac{1 - \sin x}{1 + \sin x}} + \sqrt{\frac{1 + \sin x}{1 - \sin x}}\] is equal to
If x is an acute angle and \[\tan x = \frac{1}{\sqrt{7}}\], then the value of \[\frac{{cosec}^2 x - \sec^2 x}{{cosec}^2 x + \sec^2 x}\] is
If tan θ + sec θ =ex, then cos θ equals
The value of \[\cos1^\circ \cos2^\circ \cos3^\circ . . . \cos179^\circ\] is
Find the general solution of the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
4sinx cosx + 2 sin x + 2 cosx + 1 = 0
Write the solution set of the equation
The smallest value of x satisfying the equation
If \[\cos x + \sqrt{3} \sin x = 2,\text{ then }x =\]
A solution of the equation \[\cos^2 x + \sin x + 1 = 0\], lies in the interval
The number of values of x in [0, 2π] that satisfy the equation \[\sin^2 x - \cos x = \frac{1}{4}\]
If \[e^{\sin x} - e^{- \sin x} - 4 = 0\], then x =
If \[\cos x = - \frac{1}{2}\] and 0 < x < 2\pi, then the solutions are
Find the principal solution and general solution of the following:
sin θ = `-1/sqrt(2)`
Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°
cos 2x = 1 − 3 sin x
Solve the following equations:
2cos 2x – 7 cos x + 3 = 0
Choose the correct alternative:
If f(θ) = |sin θ| + |cos θ| , θ ∈ R, then f(θ) is in the interval
Choose the correct alternative:
`(cos 6x + 6 cos 4x + 15cos x + 10)/(cos 5x + 5cs 3x + 10 cos x)` is equal to
Solve 2 tan2x + sec2x = 2 for 0 ≤ x ≤ 2π.
If sin θ and cos θ are the roots of the equation ax2 – bx + c = 0, then a, b and c satisfy the relation ______.
The minimum value of 3cosx + 4sinx + 8 is ______.
Number of solutions of the equation tan x + sec x = 2 cosx lying in the interval [0, 2π] is ______.
